Design of ER damper for recoil length minimization: A case study on gun recoil system - De Gruyter
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Journal of the Mechanical Behavior of Materials 2022; 31: 177–185
Research Article
Nguyen Huu Phan, Santosh R. Patil*, Sanjaykumar Gawade, Shailesh S. Shirguppikar,
Nguyen Trong Ly, Nguyen Chi Tam, and Le Thi Phuong Thanh
Design of ER damper for recoil length
minimization: A case study on gun recoil system
https://doi.org/10.1515/jmbm-2022-0017 is within the allowable range of 150 mm. It is shown that
received September 22, 2021; accepted April 07, 2022 the rate of firing can be increased by decreasing the recoil
Abstract length.
Purpose ‒ Recoil length minimization is always been a Originality and value ‒ The novel procedure for the
top concern in various structural, industrial, and defence design of ER damper outlined in this work will be helpful
applications. The traditional passive recoil system is not for any recoil length minimization problem.
able to respond quickly to the changes in the impact Keywords: design parameters, ER damper design, dynamic
force. These limitations can be overcome by introducing range, recoil system, total damping force, dynamic systems,
a semi-active recoil system, which comprises an intelli- active damping
gent fluid damper.
Design, methodology, and approach ‒ The electro-
rheological (ER) fluid, which responds to the applied
electric field and exhibits high yield strength, will be a 1 Introduction
proper damper for the recoil system. An ER damper can
bring back the vibrating system to its equilibrium in a The selection of appropriate electrorheological (ER) fluid
brief period. In this article, the general design procedure with desired yield strength and post-yield viscosity is a
of an ER fluid semi-active damper has been developed, prerequisite of the design process of an ER damper. As
which is suitable for a recoil system. The equations of the response time of ER fluids (in milliseconds) is greater
damping forces (viscous, quadratic, and ER) are modified than magnetorheological (MR) fluids, ER fluids have been
in terms of geometric parameter, namely the piston dia- selected for the application of gun recoil system. The
meter (DP), which can be selected to obtain the desired barium titanyl oxalate (BTO)-based ER fluid is selected
dynamic range (greater than two) and optimum damping to exhibit a yield strength of 20 kPa at 3 kV/mm. The
force. With the MATLAB software, the damper and spring design of ER fluid damper within certain constraints of
specifications are fixed to meet the required conditions, dynamic range and damping force is carried out. Also,
viz. the dynamic range should be greater than two, and calculations of recoil parameters, damper specifications,
the total damping and spring force should counter-recoil and the development of modified damper force formulae
the system. in terms of piston diameter for the general design process
Findings ‒ Results obtained for a case study of gunfire of ER damper have been carried out. The recoil mechanism
conclude that the recoil system developed using design considered here is of hydro-spring type in which a damper
specifications exhibits desired performance with max- is incorporated with ER fluid with a recuperator as a
imum recoil of 75.59 mm at 80°, angle of elevation, which spring. In the design of ER damper, the maximum impact
force for the respective charge (firing a projectile) is taken
as an input. The recoil force and recoil velocity are calcu-
* Corresponding author: Santosh R. Patil, Department of lated and are used in the design process. Though the
Mechanical Engineering, Rajarambapu Institute of Technology, spring stiffness is calculated by using impact force equa-
Rajaramnagar, India, e-mail: santosh.patil@ritindia.edu tions, the stiffness of this system is adjusted to avoid
Nguyen Huu Phan, Nguyen Trong Ly, Nguyen Chi Tam, vibration chattering. The damper rod size is fixed by
Le Thi Phuong Thanh: Faculty of Mechanical Engineering,
using buckling theory, and by using empirical relation,
Hanoi University of Industry, Hanoi, Vietnam
Sanjaykumar Gawade, Shailesh S. Shirguppikar: Department of
damper diameter is fixed to meet criteria like dynamic
Mechanical Engineering, Rajarambapu Institute of Technology, range and total damping force. For this purpose, simple
Rajaramnagar, India MATLAB codes are generated and run to fix these criteria’
Open Access. © 2022 Nguyen Huu Phan et al., published by De Gruyter. This work is licensed under the Creative Commons Attribution 4.0
International License.
178 Nguyen Huu Phan et al.
piston diameter. Other parameters of the damper are more than two and producing the required damping
determined using empirical relations. In many applica- force. The better controllability over the structure, such
tions where recoil length minimization is paramount, as battlefield gun, has been achieved; it is necessary to
this general design procedure of the recoil system will develop an ER damping force more significantly than the
be helpful. In the present study, the recoil system designed force created by a viscous damper. The dynamic range is
has been applied as a case study to recoil minimization of defined considering these forces, which is essential for
battlefield gun. better controllability. The MATLAB codes are generated
Tian [1] derived a powerful yield strength equation, and run to fix the piston diameter. The remarkable achieve-
which can be used for selecting the ER fluid for industrial ment of the proposed ER damper-based recoil system is that
applications. Xianxiang et al. [2] proposed mechanisms it showed percentage reduction in recoil mass displacement
of the ER effect. Laszlo et al. [3] investigated different as 92% with respect to technical report by US ARDE and 43%
properties of two ER fluids to check their suitability in compared to recoil system incorporated with MR damper at
gun recoil application. Tao [4], a pioneer in introducing 63° of firing angle.
the ER fluid with a yield stress of more than 100 kPa,
studied the behaviour of physical phenomena of ER
mechanism. Li et al. [5] synthesized giant electrorheolo-
gical (GER) effect fluids. The fluid exhibits anti-sedimen- 2 Design of an ER damper
tation property with a yield strength of 194 kPa. Singh
and Wereley [6] developed a control mechanism for the
subjected to transient excitation
minimum transfer of gun recoil load to the structure and
The general procedure of the design of ER damper sub-
optimized the gunfire rate by introducing an MR damper
jected to external transient force excitation is presented
in the semi-active control system. Wen et al. [7] carried
in this section. The suitable ER damper has been designed
out synthesis and characterization of GER fluid with the
by the iterative method, considering various parameters,
yield strength of 130 kPa at 5 kV/mm. Li and Wang [8]
which typically affect the performance of ER fluid damper.
developed a recoil system with an MR absorber and have
The dynamic range is the most crucial parameter con-
shown an improvement in the capacity of the absorber.
cerned with the damper, which controls such a fluid
Carlos and Lopez [9] have proved that semi-active suspen-
damper. The dynamic range strongly depends on damper
sion systems with ER damper can dissipate more energy.
parameters like piston diameter, gap thickness, and length
Xiangcong et al. [10] designed and analysed an intelligent
of recoil. During the designing of the damper, emphasis
gun recoil system with a damper. Mehdi et al. [11] studied
has been given to these parameters to maintain the
the application of MR damper for controlling recoil
required controllability and force. The design process
dynamics. Zekeriya et al. [12] carried out a performance
is carried out by considering the maximum transient
analysis of the flow mode MR damper having the annular
input to the recoil system. Design details are given in
gap in the piston. Kathe et al. [13] determined venting
the following sub-sections.
time, impulse reduction estimate, and bore heating reduc-
tion for 120 mm bore diameter gun. Dixon [14] developed a
mathematical model for a damping system considering the
quadratic damping coefficient. Shams et al. [15] have car- 2.1 Non-linear damping force equations to
ried out the coupled computational: fluid dynamics (CFD) design ER damper
and finite element analysis (FEA) analysis of hydraulic
shock absorber valve behaviour. The equation of motion of a recoil system using a semi-
Because of the scope and depth of this research, there active ER damper is given as:
is no study in the literature on improving the perfor-
mẍ + FD + kx = FF(t ) , (1)
mance by minimizing recoil length using an intelligent
recoil mechanism. The major contribution of the present where FD is the non-linear damping force provided by the
work is a novel design process of ER damper. The pro- ER damper and is given as:
posed design process can be helpful in recoil system
FD = CDVd + CQVd2 + FER . (2)
applications. From the literature, it has been observed
that there is no such systematic design process readily The first term on the right-hand side of equation (2)
available. The main challenge is to design a recoil system represents viscous damping force, the second term repre-
within the constraints of maintaining a dynamic range of sents quadratic damping force, and the third term is the ER
Design of ER damper for recoil length minimization on gun recoil system 179
damping force [14]. Here, CD is the coefficient of viscous controlling force is achieved by varying the electric field,
damping and CQ is the coefficient of quadratic damping. as the orifices are not provided in the main piston. The ER
With this value of FD, Eq. (1) becomes: phenomenon is achieved by maintaining an air gap less
than 1 mm between two-cylinder electrodes. High DC
mẍ + CDVd + CQVd2 + FER + kx = FF(t ) . (3)
voltage is applied across these electrodes.
Eq. (3) is used when the firing angle, θ is zero. When θ The viscous damping force is given as follows:
is not equal to zero, the equation of motion (3) is modified 2
6 μLFA APA
to take into account the effect of the component of grav- FDV = CDVd = 3
Vd, (5)
πRFA tFA
itational force in the direction of the motion. The mod-
ified Eq. (4) is as follows: where µ is the viscosity of ER fluid and APA is the cross-
sectional area of piston annulus.
mẍ + (CD1x + CD2x 2 + FER )signẋ + kx
(4) π 2
= FF(t ) + mg Sinθ. APA = (DP − DR2 ) . (6)
4
The cross-sectional area of the fluid annulus is
obtained as:
2.1.1 Problem of the requirement of a priori knowledge
of ER damper piston diameter AFA = 2πRFA tFA. (7)
Assuming geometric relations, diameter of rod, DR =
In the development of the recoil system, the design of an 0.6 DP and the radius of fluid annulus, RFA = 0.6 DP.
ER damper is the most important one, as shown in Figure 1. Eq. (5) is modified by using Eqs. (6) and (7) with the
From a review of the literature on the design and develop- aforementioned geometric relations as:
ment of an ER damper, it is seen that the main problem
encountered is the requirement of a priori knowledge of 6 × 0.409 π ⎞⎛ μ LFA Vd ⎞ 3
FDV = ⎛ ⎜
3
⎟DP . (8)
the damper piston diameter. To overcome this problem, in ⎝ 16 × 0.6 ⎠⎝ tFA ⎠
this article, the formulae for viscous damping, quadratic
Thus, Eq. (8) is deduced in terms of piston diameter.
damping, and ER damping are expressed in terms of piston
All other terms like the length of the fluid annulus, the
diameter.
viscosity of fluid, and gap maintained between two elec-
trodes are fixed and assuming the maximum piston veloc-
ity as 2 m/s; the piston diameter can be adjusted to achieve
2.1.2 Modification of equations for FDV, FDQ, and FER
the required damping force. Similarly, equation of quad-
ratic damping force can be deduced in terms of piston
The annular flow design approach is employed while
diameter as:
designing ER damper, as shown in Figure 1, and the
1
FDQ = CDVd2 = ραfA2 APA Vd2, (9)
2
where ρ is the density of the fluid and α is the kinetic
energy correction factor. fA the area factor is given as:
APA π / 4(0.64 × DP2 ) Dp
fA = = = 0.1333 × . (10)
AFA 2πRFA tFA tFA
Using Eqs. (9) and (10), equation of quadratic damping
coefficient is simplified in terms of piston diameter as:
2
ρ α Vd ⎞ 4
FDQ = 0.0044⎛⎜ 2
⎟DP . (11)
⎝ tFA ⎠
Figure 1: Cut section model of ER damper. E – applied voltage to the Eq. (11) represents the quadratic damping force in
electrodes, LFA – length of the fluid annulus, RFA – radius of fluid
terms of piston diameter.
annulus, DFA – diameter of the fluid annulus, tFA – thickness of fluid
annulus, tOC – thickness of outer cylinder, tIC – thickness of inner
The ER damping force equation is also deduced in
cylinder, LR – length of the piston rod, and the damping force expres- terms of piston diameter. The ER force is subjected to
sions for FDV, FDQ, and FER are modified in terms of piston diameter (DP). the resulting ER effect, ultimately which depends upon
180 Nguyen Huu Phan et al.
the applied electric field between the gap of the elec- Furthermore, the thicknesses of the inner and outer
trodes. The ER effect produces yield shear stress (τER) in cylinders are determined by using pressure vessel theory.
ER fluid, which acts over the ER fluid trapped between the For the inner cylinder, inner diameter (Di) is taken as the
two electrodes. The ER shear force acting over the cross- diameter of the piston. The dimensions of the piston rod
sectional area of the fluid annulus is due to the pressure are obtained by using the theory of buckling.
drop at the fluid annulus. Thus, resisting pressure acting
over the cross-sectional area of piston annulus is given as:
2 LFAτER 3 A case study on gun recoil system
FER = APA . (12)
tFA
The general design process of a recoil system discussed in
Upon simplification FER is given as: Section 2 is implemented to design the recoil system of a
battlefield gun. The ER damper and mechanical spring
L τ
FER = 1.005 ⎛ FA ER ⎞DP2 .
⎜ ⎟ (13) specifications are obtained based on the dynamics of
⎝ tFA ⎠
the gun recoil system and the general design approach.
Eq. (13) represents the ER damping force in terms of
piston diameter.
3.1 Gun recoil system and its dynamics
2.1.3 Development of a MATLAB problem to determine A schematic model of the typical gun recoil system is
the piston diameter DP shown in Figure 2. When the gun fires a projectile, it
leaves a barrel due to high pressure created behind it
A MATLAB program is developed to calculate the total by the propellant. As per Newton’s third law, the same
damping force (FD), which comprises viscous, quadratic, pressure forces back the gun barrel. For heavy-duty guns,
and ER damping forces in terms of piston diameter (DP). it is necessary to design recoil system with spring force
The diameter of the piston will be determined from a “k” and damper with high damping coefficient “c.”
specific range of values with a fixed step size. The value
of one such piston diameter from the range of value will
be selected such that the total force obtained is approxi- 3.2 Parametric analysis of gun recoil system
mately equal to the input firing force.
The peak force generated by a projectile of gun is of the
order of 460 kN [17]. Considering this as maximum input
2.2 Testing suitability of damper diameter force to the recoil system, the design process is carried out.
Calculations have been performed on separate excel sheets
While obtaining a piston diameter of ER damper, it is using empirical equations. The results obtained are as fol-
necessary to check the dynamic range ratio and total lows: spring stiffness k = 1,850 kN/m, critical damping coef-
damping force for maximum impact force. The dynamic ficient cc = 153.280 kN/s, and the damping coefficient, c =
range ratio is the ratio of damping force obtained during 91.96 kN/s. Assuming maximum damper piston velocity as
the off-state condition to applied electric field condition. 2 m/s, the total damping force, Fd is obtained as 184 kN.
It can be given as [16]: Total recoil force = Damping force + spring force
FER = 184 + 277.5 = 461.5 kN.
DR = 1 + . (14)
FVD + FDQ The total recoil force is nearly equal to the maximum
In order to get a significant effect of ER force, it is firing force (460 kN).
required to maintain a dynamic range more than or equal
to 2. At the same time, the ratio of viscous damping force 3.3 Design calculations of ER damper
to ER damping force should be less than 1. Thus, the
piston diameter can be fixed to fulfil both the conditions As described in Section 2.1.3, the diameter of the piston is
of dynamic range and maximum recoil force. determined from the range of values: 50–225 mm with a
The radius of the fluid annulus is given as: step size of 1 mm. The value of one such piston diameter
RFA = 0.6 × DP . is selected such that the total damping force obtained is
approximately equal to input firing force and dynamicDesign of ER damper for recoil length minimization on gun recoil system 181
Figure 2: Schematic model of gun recoil system. 1 – Britch, 2 – barrel, 3 – caliber (projectile), 4 – muzzle brake, 5 – gun chasis, 6 – wheel,
7 – trail, 8 – ER damper, 9 – mechanical spring, 10 – gun carriage, and 11 – recoil system.
range is equal to 2. The dynamic range for the calculated By using geometric relation, DR = 0.6 × DP ; DP is cal-
diameter of the piston (140 mm) is 2, as shown in Figure 3. culated as 137.08 mm.
The total damping force for different values of piston dia- Thus, the diameter of the piston is rounded off to the
meter is shown in Figure 4. value of 140 mm. The dynamic range for 140 mm diameter
Simultaneously, of piston is nearly equal to 2 as shown in Figure 3 and the
i) Piston rod diameter is determined by using buckling total damping force is 310 kN as shown in Figure 4.
theory. The radius of fluid annulus is given as RFA = 0.6 × DP =
ii) For calculated piston diameter, the dynamic range 0.6 × 140 = 84 mm.
and damping force are checked. The inner diameter of inner cylinder is exactly equal
iii) The buckling length for stroke length of 150 mm is to piston diameter, Dii = 140 mm. The material selected
determined as, Lengthbuckling = 450 mm. for inner cylinder is mild steel.
The thickness of the cylinder can be determined as:
Using this calculated buckling length and consid- 29.88 × 140
t= = 14.92 ≅ 15 mm.
ering the factor of safety as 2, for the stroke of 150 mm 2 × 140.16
the piston rod diameter is calculated as 82.25 mm. It will The outer diameter of inner cylinder, Doi = Dii + 2t =
sustain maximum load of 460 kN without buckling. 170 mm.
Figure 3: Dynamic range and range ratio vs different values of piston diameter (m).182 Nguyen Huu Phan et al.
Figure 4: Total damping forces (Ft) vs different values of piston diameter (m).
Gap between two cylinders is already decided as time is recorded for different values of angles at which the
0.7 mm. The dimensions of outer cylinder are: gun is oriented.
Inner diameter of outer cylinder (Dio) = 170 + 1.4 = For this purpose, Eq. (4) of recoil mass is rear-
171.4 mm. ranged as:
Outer diameter of outer cylinder (Doo) = 171.4 + 2t = 1
201.4 mm. ẍ (t ) = {FF (t ) − kx + mg Sinθ
m (15)
All the specifications of the designed ER damper are
− (CD1 x + CD2 x2 + FER ) sign (ẋ )} .
summarized in Table 1.
The simulation based on designed ER damper is car- The Simulation Model is developed based on Eq. (15)
ried out for an application concerning gunfire. using Simulink blocks. A Simulink code is developed
using various inputs such as impact force, ER fluid char-
acteristics, spring and damper specifications, and recoil
4 The effect of angle of elevation on mass. The resulting output is presented in graphical
form, the velocity vs. displacement, displacement vs
the gun recoil system time, damping force vs time, and spring force vs time.
performance: a simulation study The performance of the recoil system changes with firing
elevation angle θ. The calculations of the projectile range
The 3D model of ER damper with designed specifications and its height for different firing elevation angles θ
is developed. With this 3D model, performance evalua- (0–80°) have been carried out. The range for the projec-
tion of recoil system in MATLAB/Simulink environment tile is maximum (32.315 km) at an elevation angle of 45°.
has been carried out. The recoil displacement in terms of Hence, the results are obtained for a firing elevation
the desired value of stopping distance and total process angle of 45°. The results of the analysis are given in
Table 1: Specifications of designed ER damper
Sr. no. Design parameter Notations Dimension (mm)
1 Piston rod diameter DR 82.25
2 Piston diameter DP 140
3 Inner diameter of inner cylinder Dii 140
4 Outer diameter of inner cylinder Doi 170
5 Gap between cylinders/electrode gap tFA 0.7
6 Inner diameter of outer cylinder Dio 171.4
7 Outer diameter of outer cylinder Doo 201.4Design of ER damper for recoil length minimization on gun recoil system 183 Figure 5: Velocity vs displacement at 45° firing angle. Figures 5 and 6. Figure 5 presents the recoil mass that covered by recoil mass during its motion and is 69.32 mm, comes back to its’ equilibrium position or at battery which is less than the limiting recoil-stopping distance of position. Figure 6 displays the maximum displacement 150 mm. Figure 6: Displacement vs time at 45° firing angle.
184 Nguyen Huu Phan et al.
Table 2: Displacement and yield strength at different firing angles 95% with respect to technical report and 55% compared
to recoil system incorporated with MR damper at 0° of
Firing angle in Yield strength of Max. displacement by firing angle and it is 92 and 43%, respectively, at 63° of
degrees ER fluid (Pa) Simulink model (mm) firing angle.
0 5,100 54.55
10 4,650 58.02
20 4,225 61.50
30
40
3,850
3,525
64.85
67.93
6 Conclusion
45 3,400 69.32
50 3,250 70.69 In this research, we aimed to design the ER fluid damper
70 2,900 74.59 for a recoil system. The equations of damping forces
80 2,825 75.59 (viscous, quadratic, and ER) are modified in terms of
geometric parameter, namely the piston diameter (DP).
The value of one such piston diameter is used such that
For the sake of completeness of the analysis, the the desired results like dynamic range greater than 2 and
values of maximum displacement at different firing ele- better controllability can be achieved. The design is also
vation angles of 0°, 10°, 20°, 30°, 40°, 45°, 50°, 70°, and checked for piston rod buckling, and it is found safe.
80° have been obtained and are given in Table 2. Table 2 The great success of this study is to increase the firing
also gives yield strength of ER fluid required at respective rate by decreasing the recoil length, i.e. by restricting
firing angle to generate sufficient damping force so that piston displacement of the innovative damper to 75 mm.
the mass will recoil within the restricted distance of The designed damper is developed for the semi-active
150 mm and will come back to its equilibrium position. gun recoil system to reduce the recoil length, cycle time,
It can be observed from Table 2 that the maximum and firing rate. The experimental performance of the pro-
displacement of recoil mass is achieved at 80°. The recoil posed recoil system reveals that the recoil displacement is
mass displacement increases with the increase of angle varying from 40 to 60 mm with the recoil time of 0.25–0.35 s
of elevation. The maximum displacement even at an from 10° to 80° of firing inclination. Also, it showed signifi-
angle of 80° is less than the allowable displacement of cant reduction in recoil displacement as 92% compared to
150 mm. Therefore, the specifications obtained for the technical report of US ARDE and 43% to recoil system with
developed ER damper are satisfactory to achieve the MR damper at 63° firing angle. It is shown that the firing
desired performance. rate can be increased by decreasing the recoil length for this
designed recoil system, and hence this is a viable alternative
to counter the vibrations in the gun structure to improve the
5 Comparative study efficiency of the weapon.
The modified model is helpful to design ER damper
Based on this comparative study presented in Table 3, it for any application where recoil minimization is the
is found that there is a large reduction in recoil displace- prime objective.
ment, hence the cycle duration will reduce and the
number of fires per minute will increase significantly.
The proposed ER damper-based recoil system exhib-
ited percentage reduction in recoil mass displacement as Nomenclature
BTO barium titanyl oxalate
Table 3: Comparison of recoil mass displacement
DR piston rod diameter
DP piston diameter
Firing Recoil mass displacement in (m) Dii inner diameter of inner cylinder
inclination in Doi outer diameter of inner cylinder
Technical MR damper Proposed ER
degrees Dio inner diameter of outer cylinder
report recoil damper recoil
system system Doo outer diameter of outer cylinder
E applied voltage to the electrodes
0 1.219 0.1225 0.05455
ER electrorheological
63 0.9525 0.1296 0.07342
FDV viscous damping forceDesign of ER damper for recoil length minimization on gun recoil system 185
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